First day in London itinerary when staying at Park Plaza County Hall?

Is it a good plan to walk along the south side of the river, stopping at the Borough Market for a bite, then going to the Tower? Are the river ferries DEPENDABLE?

Yes. And YES. Though the capitalisation is weird.

read horrible reviews by people who waited and waited because they had planned to use the river ferries to get from one spot to another.

These are the people who can’t read a simple timetable.

Should we stop and do something along the way to the Tower of London or keep a move on it?

No idea

Should we walk or use some kind of transportation to be getting from the hotel to Tower? It's a bit of a long walk, but I read there are low emissions zones where taxis can't go. I'm uncertain about whether I want to take my son on the metro/tube/underground system, honestly. I've read it can be busy/loud and I'm not sure how safely he can negotiate anything that could happen like getting separated.

That is ridiculous

I also don't need us dealing with migraines from noise.

Seriously?

What is the best plan for getting from the hotel to the Tower, possibly with some lunch, if we don't want to use the metro/tube/underground?

Walk. Or bus.

Would it be more scenic to do the walk cross over say at the Millenium Bridge, eat somewhere on that side, then keep walking? If we go to the Borough Market, we could cross over on London Bridge and then use the Tower Bridge on the return.

Is there another way to do this I'm not realizing?

No

Is Uber Boat more reliable than the regular river tours?

Yes

Oh and we've agreed we're not interested in trying to see the changing of the guard.

Don’t. It’s tedious.

I thought there was some logic to it in fact, because we could be arriving at the Tower while the masses are trying to watch the changing of the guard at Buckingham Palace.

There are not masses Because it is tedious

And a final question. How much of an abomination would it be to go to the London Dungeon? Taking a teenager mind you.

A total abomination

The walk along the South Bank is great, and a really good way to see London. Go as far as you feel able - it will take you past the National Theatre and the Tate Modern (both free to pop in, use toilets, buy a cup of tea or coffee if needed).

At the Millennium Bridge (by the Globe Theatre and the Tate Modern) you can cross over to see St Paul’s or stay on the South Bank for Borough Market, Southwark Cathedral etc.

If you get bored of walking or exhausted, catch one of the boats or you could go a little bit south of the river path to the nearest road and hail a black cab. They can go everywhere in London (except on footpaths). The emission zone does not affect them - you’ve been reading some weird stuff! Or get a bus. Or a tube from Southwark or London Bridge or wherever you find yourself. Or a boat.

Actually if you’re exhausted once you reach the Millennium bridge, walk across to St Paul’s and you would find it easy to hail a black cab nearby to take you to the Tower (or get the bus).
The masses don’t all watch Changing of the Guard. All of central London is busy, but people cope with it. Just ask someone if you find yourself lost or confused.

If you are somebody from a rural area or who is not used to public transport the tube can be intimidating, especially with a teenager who needs shepherding.

But it is actually pretty straightforward.

Let's see.

In central London all Underground (the proper name) routes are are actually underground and they runs in round tunnels - hence the nickname Tube. In suburban areas the trains actually run mostly on the surface - there are more miles of surface than tunnel - but the whole system is named the Underground and in slang called the tube. Metro is a train system in the northeast of England and the name of the Paris underground/overground system, the term Metro is never used in London.

The tube is very frequent. During the day it will be rare for you to wait more than 3 minutes for a tube train. And they are fast, much faster than walking or driving or taking a bus or boat. There are several lines, each with a name and a colour. Have a look on the official map to see what I mean. https://tfl.gov.uk/maps/track/tube At interchanges you can follow signs to another line, the signs are both in words and colour coded. Entrances to the tube network are clearly marked on the street.

It is always a good idea to have an emergency plan in any city in case (very rarely) you get separated and one gets on and the other doesn't, or one gets off and the other doesn't. Could be bus, could be boat, could be tube - anything. Everybody should have a card with them with the name and address of the hotel. Best thing if somebody gets on or off leaving one behind is: First - don't panic. Then whoever is on by themselves gets off at the next stop and waits on the platform at the same place at that next stop. Then those left behind get on the next train/bus/boat and go one stop and get off. Reunion!! and then get on with the day. It is rare, and having a plan takes away anxiety.

Questions?

The river boats are reliable, but understand that as with any form of transportation things can happen. If I turned up at a dock I would expect the next boat at the time advertised on the sign.

A strong tide or storm can affect boat times.

London Dungeon - never did it, never will. Maybe a teenager would enjoy. Don't know.